If the home/root partition is a physical or logical volume you most certainly can leave that decrypted while encrypting other volumes. The system could not boot if that were the case as the efi partition cannot be encrypted.

I was curious about this and found this KDE forum post that might help. Looks like you don’t even need a script.

I’m not sure how it works for KDE and sddm but on gdm it is possible to copy the monitors.xml config file to a certain directory to fix that. After doing so, the login and lock screen settings are synced between the desktop environment and display manager. Not sure how to do it for sddm but I’m sure there’s a way, maybe a script with the correct xrandr commands could solve that.

Edit: monitors.xml, not x11.conf